724 X. ON THE STRUCTURE OF 'MATTER' |
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boundary conditions which have to be satisfied by the solution of a differential equation. In the new wave mechanics there is also a differential equation representing the Schrfidinger wave equation.
^{14}Section G. Structural aspects of the new theories.We should notice the important distinction between the two structural types of these theories. The extensional matrix theory can hardly be visualized, with all the consequent advantages and disadvantages. The wave mechanics can be visualized. From what we already know of the structure and working of the nervous system, we see that the wave mechanics will have a
creative element and the matrix mechanics will remain an important checking method.At present, all these new theories seemingly have blended or perhaps it would be better to say that they have been translated from one language to another and all the workers in this field work from all angles.
It should be mentioned also, that Einstein, Bose, Jordan, and others, work from the point of view of
statistics, and that these methods, too, are being retranslated and connected with the rest of the new theories.The new wave mechanics evades the difficulties of the matrix calculus and brings the new mechanics within the scope of the highly developed analysis of the theory of differential equations. It also enlists the creative aspects of 'intuition', 'visualization', .
Concluding our consideration of the subject, three remarkable aspects of the wave mechanics must be referred to. We are already acquainted with the term 'action'. It appears that the main point of the passing from the old mechanics to the new was the stroke of genius of de Broglie, when he divided action by the fundamental constant
h with some definite numerical factor which then gives us the phase. In the expression for $, the energy appears as the 'time' component of a space-time vector whose 'space' components are those of the momentum. When this vector is divided by h, its components become the frequency, or the number of waves which each axis cuts per centimetre.These are the methods by which we can use differential equations, whereby the older discontinuities disappear and the particle is represented as a group of reinforcing waves.
^{16}From this point of view we also come to the conclusion that the 'conservation of energy', which was very valuable in the old days, is perhaps only a gross macroscopic generalization and will give place to a newer and more fundamental notion of the conservation of
frequency or 'times'.^{16}It has been already mentioned that the newer mechanics must be represented in accordance with statistical data, probabilities, with due attention paid to the theory of errors , . While these requirements have very little to do with the world around us, they are unconditionally required by our nervous structure, which is, after all, the general author of all our 'knowledge' and 'theories'. Let us be candid about it; there is no such thing as 'knowledge' outside of a nervous system, and therefore the neurological requirements, as already |
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